O is the incentre of `Delta ABC` and `angle A=30^(@)`, then find `angle BOC`.

Answer

To find angle BOC in triangle ABC where O is the incenter and angle A is given as 30 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Incenter**: The incenter (O) of a triangle is the point where the angle bisectors of the triangle intersect. It is also the center of the circle inscribed in the triangle.

2. **Identify the Angles**: We know that angle A = 30 degrees. We need to find angle BOC.

3. **Use the Formula for Angle BOC**: The formula for finding angle BOC when O is the incenter is:
\[ \text{Angle BOC} = 90^\circ + \frac{\text{Angle A}}{2} \]

4. **Substitute the Value of Angle A**: Since angle A = 30 degrees, we can substitute this value into the formula:
\[ \text{Angle BOC} = 90^\circ + \frac{30^\circ}{2} \]

5. **Calculate the Half of Angle A**: Calculate \(\frac{30^\circ}{2}\):
\[ \frac{30^\circ}{2} = 15^\circ \]

6. **Add to 90 Degrees**: Now, substitute this back into the equation:
\[ \text{Angle BOC} = 90^\circ + 15^\circ = 105^\circ \]

7. **Final Answer**: Therefore, angle BOC is equal to 105 degrees.

### Conclusion:
The value of angle BOC is **105 degrees**.

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